Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables

Aazami, Amir Babak; Keeton, Charles R.; Petters, Arlie O.

doi:10.1063/1.3642616

Cited by 53 publications

(41 citation statements)

References 22 publications

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“…(iii) Finally, letting γ = w = 1, we recover the deflection of light in a Kerr geometry. Our result for the deflection angle is consistent with previous studies [22][23][24][25][26][27][28][29]. It is important to realize that our method applies only for relativistic particles, i.e.…”

Section: A Deflection Anglesupporting

confidence: 91%

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

et al. 2019

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We study the gravitational deflection of relativistic massive particles by Janis-Newman-Winicour (JNW) spacetimes (also known as a rotating source with a surface-like naked singularity), and a rotating Kerr-like wormholes. Based on the recent article [K. Jusufi, Phys.Rev. D 98, 064017 (2018)], we extend some of these results by exploring the effects of naked singularity and Kerr-like objects on the deflection of particles. We start by introducing coordinate transformation leading to an isotropic line element which gives the refraction index of light for the corresponding optical medias. On the other hand, the refraction index for massive particles is found by considering those particles as a de Broglie wave packets. To this end, we apply the Gauss-Bonnet theorem to the isotropic optical metrics to find the deflection angles. Our analysis shows that, in the case of the JNW spacetime the deflection angle is affected by the parameter 0 < γ < 1, similarly, we find that the deformation parameter λ affects the deflection angle in the case of Kerr-like wormholes. In addition to that, we presented a detailed analysis of the deflection angle by means of the Hamilton-Jacobi equation that lead to the same results. As a special case of our results the deflection angle of light is recovered. Finally, we point out that the deflection of particles by Kerr-like wormholes is stronger compared to JNW spacetime, in particular this difference can be used to shed some light from observational point of view in order to distinguish the two spacetimes.

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Section: A Deflection Anglesupporting

confidence: 91%

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

et al. 2019

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“…We will only illustrate the procedure and results in the KN spacetime because setting its charge to zero will yield the corresponding results in the Kerr metric. To our knowledge, the deflection angle in Kerr spacetime has been known to fourth order in 1 x 0 and 1 b for lightlike rays [72,73].…”

Section: A Weak Deflection Angle In Equatorial Plane Of the Kerr Andmentioning

confidence: 99%

The perturbative approach for the weak deflection angle

Jia

2020

Eur. Phys. J. C

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Both null and timelike rays experience trajectory bending in a gravitational field. In this work, we systematically develop a perturbative method to compute the deflection angle of rays with general velocity v in arbitrary static and spherically symmetric spacetimes and in equatorial plane of arbitrary static and axisymmetric spacetimes. We show that the expansion in the large closest approach x0 limit depends on the asymptotic behavior of the metric functions only, and the generated integrand is always integrable, resulting in a deflection angle in a series form of either x0 or b, the impact parameter. Using this method, the deflection angles as series of both x0 and b are found in Schwarzschild, Reissner-Nordström and Kerr-Newman spacetimes to 17-th, 15-th and 6-th orders respectively, for both lightrays and particles with general velocity. The effects of the impact parameter, velocity and other parameters of the spacatimes are briefly analyzed. Moreover, we show that for spacetimes whose metric functions are only asymptotically known, the deflection angle in the weak field limit can also be calculated. Furthermore, it is shown that the deflection angle in general static and spherically symmetric spacetime and equatorial plane of static and axisymmetric spacetime to the lowest non-trivial order, depends only on the impact parameter, velocity of the particle, and the effective ADM mass of the spacetime but not on other parameters such as charge or angular momentum. These deflection angles are used in an exact gravitational lensing equation and the corresponding apparent angles of the images of the source are also solved perturbatively.

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“…Therefore, we only provide some hints of its gravitational lensing signals. More sophisticated investigations with inclusion of its spin in the weak [97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113] and strong [114][115][116][117][118] deflection lensing as well as general relativistic magnetohydrodynamics of plasma are indeed needed.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Weak and strong deflection gravitational lensing by a renormalization group improved Schwarzschild black hole

Xie

2019

Eur. Phys. J. C

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Weak and strong deflection gravitational lensing by a renormalization group improved Schwarzschild black hole is investigated and its observables are found. By taking the supermassive black holes Sgr A* and M87* respectively in the Galactic Center and at the center of M87 as lenses, we estimate these observables and analyse possibility of detecting this quantum improvement. It is not feasible to distinguish such a black hole by most observables in the near future except for the apparent size of the shadow. We also note that directly using measured shadow of M87* to constrain this quantum effect requires great care.

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Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables

Cited by 53 publications

References 22 publications

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

Distinguishing rotating naked singularities from Kerr-like wormholes by their deflection angles of massive particles

The perturbative approach for the weak deflection angle

Weak and strong deflection gravitational lensing by a renormalization group improved Schwarzschild black hole

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